Next, we develop a variational EM maximum likelihood algorithm [1]}, [2]} to infer the deterministic parameters \(\mathbf {\mu }_{k}\) , \(\mathbf {\Sigma }_{k}\) , and \(\Theta _{kl}\) . The main objective is to maximize the likelihood of the observations under the model. The algorithm comprises two alternating steps: i) Expectation step (E-step), where we integrate out the latent variables, ii) Maximization step (M-step), where we optimize the model parameters to maximize the marginal likelihood.
